# Full text of "Analytical Mechanics"

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```106                      ANALYTICAL MECHANICS
A^rtrt.2
(b)   The normal kinetic reaction has a magnitude — and
has a direction opposite to that of the normal acceleration. In other words it has the same direction as the radius of curvature, i.e., away from the center of curvature,
Normal kinetic reaction =----•               (IV")
(c)   The total kinetic reaction has a magnitude m y v2+ ~
p" and has a direction opposite to that of the total acceleration,
Total kinetic reaction = — wv.                (IV)
FORCE   EQUATION".
96. Force Equation. — Combining (A/) and (IV) and denoting the resultant force by F we obtain
(V) = mv.J
Equation (V) is called the force equation. It states that the resultant force acting upon a particle equals the product of the mass by the acceleration and has the same direction as the latter.
/       v1 Since the magnitude of v is y v2 + ~;>; ^e f°rce equation
takes the following form when stripped of its vector notation :
>                      (VI)
In- equation (VI) v represents that part of the acceleration which is due to the change in the magnitude of the velocity
v2
and — represents that part which is due to the change in the . P
direction.*
97.  Component-force Equations. — Splitting equation (V) into two component equations which correspond to the di-
* See p. 94 for the tangential and normal components of V.```